scholarly journals Numerical analyses of transient natural convection of liquid metals after a step change in an external lateral magnetic field.

1990 ◽  
Vol 16 (5) ◽  
pp. 990-997
Author(s):  
Hiroyuki Ozoe ◽  
Eiji Maruo ◽  
Hiroshi Matsuo
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Liquid Metals ◽  
Step Change ◽  
Numerical Analyses ◽  
Transient Natural Convection

scholarly journals Natural Convection Flow in a Strong Cross Magnetic Field With Radiation

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
S. Siddiqa ◽  
M. A. Hossain ◽  
Suvash C. Saha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Finite Difference ◽  
Radiative Heat ◽  
Liquid Metals ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Physical Parameters

The problem of magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and optically dense gray viscous fluid along a heated vertical plate is analyzed in the presence of strong cross magnetic field with radiative heat transfer. In the analysis radiative heat flux is considered by adopting optically thick radiation limit. Attempt is made to obtain the solutions valid for liquid metals by taking Pr ≪1. Boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation (SFF) and primitive variable formulation (PVF). Nonsimilar equations obtained from SFF are then simulated by implicit finite difference (Keller-box) method whereas parabolic partial differential equations obtained from PVF are integrated numerically by hiring direct finite difference method over the entire range of local Hartmann parameter, ξ. Further, asymptotic solutions are also obtained for large and small values of local Hartmann parameter ξ. A favorable agreement is found between the results for small, large and all values of ξ. Numerical results are also demonstrated graphically by showing the effect of various physical parameters on shear stress, rate of heat transfer, velocity, and temperature.

scholarly journals Role of Induced Magnetic Field on Transient Natural Convection Flow in a Vertical Channel: The Riemann Sum Approximation Approach

2015 ◽  
Vol 20 (1) ◽  
pp. 65-85
Author(s):  
B.K. Jha ◽  
I. Sani
Keyword(s):  
Magnetic Field ◽  
Natural Convection ◽  
Vertical Channel ◽  
Convection Flow ◽  
Induced Magnetic Field ◽  
Natural Convection Flow ◽  
Transient Natural Convection ◽  
Riemann Sum ◽  
Laplace Transform Technique

Abstract This paper investigates the role of induced magnetic field on a transient natural convection flow of an electrically conducting, incompressible and viscous fluid in a vertical channel formed by two infinite vertical parallel plates. The transient flow formation inside the channel is due to sudden asymmetric heating of channel walls. The time dependent momentum, energy and magnetic induction equations are solved semi-analytically using the Laplace transform technique along with the Riemann-sum approximation method. The solutions obtained are validated by comparisons with the closed form solutions obtained for the steady states which have been derived separately and also by the implicit finite difference method. Graphical results for the temperature, velocity, induced magnetic field, current density, and skin-friction based on the semi-analytical solutions are presented and discussed.

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